因式分解

题目

因式分解
(x+2)(x-2)+16
4(x+y)^2-20(x+y)+25
a^2-b^2-4a+4b
下面计算
(2+1)(2^2+1)(2^4+1)……(2^(2n)+1)

答案

(x+2)(x-2)+16=x^2-4+16=x^2+124(x+y)^2-20(x+y)+25=(2x+2y-5)^2a^2-b^2-4a+4b=(a+b)(a-b)-4(a-b)=(a-b)(a+b-4)下面计算(2+1)(2^2+1)(2^4+1)……(2^(2n)+1) =(2-1)(2+1)(2^2+1)(2^4+1)……(2^(2n)+1) =(2^2-1)(2^2+1...